GoodBuy Inc. is a small electronics company that manufactures cell phones and digital recorders. The per-unit labor costs, raw material costs, and selling price of each product are given below. On December 1, 2008, GoodBuy has available raw material that is sufficient to manufacture 100 cell phones and 100 recorders. On the same date, the company’s balance sheet is as shown in the table below. GoodBuy’s asset/liability ratio (called the current ratio) is 20,000/10,000 = 2.
GoodBuy must determine how many cell phones and recorders should be produced during December. Demand is large enough to ensure that all goods produced will be sold. All sales are on credit, however, and payment for goods produced in December will not be received until February 1, 2009. During December, GoodBuy will collect $2000 in accounts receivable, and GoodBuy must pay off $1000 of the outstanding loan and a monthly rent of $1000. On January 1, 2009, GoodBuy will receive a shipment of raw material worth $2000, which will be paid for on February 1, 2009.
GoodBuy’s management has decided that the cash balance on January 1, 2009 must be at least $4000. To maintain its current favorable credit status, GoodBuy’s bank requires that the current ratio at the beginning of January be at least 2. To maximize the contribution to profit from December production, (revenues to be received – variable production costs), what should GoodBuy produce during December?
1 – Accounts receivable is money owed to GoodBuy by customers who have previously purchased GoodBuy products.
2 – Value of December 1, 2008 inventory = 30(100) + 40(100) = $7000.
Deliverables:
X1 = number of cell phones produced during December
X2 = number of digital recorders produced during December
January 1 cash on hand = December 1 cash on hand
+ accounts receivable collected during December
January 1 asset position = January cash position
+ January 1 accounts receivable + January 1 inventory position.
January 1 cash position = 10,000 – 50x1 – 35x2
January 1 accounts receivable = December 1 accounts receivable
+ accounts receivable from December sales
- accounts receivable collected during December.
Value of January 1 inventory = value of December 1 inventory
- value of inventory used in December
+ value of inventory received on January 1.
January 1 liabilities = December 1 liabilities – December loan payment
+ amount due on January 1 inventory shipment.
Your mathematical result should be:
X1 = 50 cell phones
X2 = 100 digital recorders
Maximum profit = $2500.
Here's all the infromation associated with the problem. Here's what I have so far:
objective: max
let x1= #of cell phones produced during december
x2= #of digital recorders produced during decmeber
x3= labor costs
x4= raw material cost
x5= cash on hand
x6= A/R
x7= inventory on hand
x8- loan
x9= rent
Subject to:
50x3+30x4 <100 (cell phones)
35x3 + 40x4 < 100 (recorders)
10,000x5 + 2000x6 - 1000x8 - 1000x9 - x3 > 4,000 (cash in hand)
Should l I have that many variables (x1, x2, x3, x4) ? And as far as my objective goes should it include what's in the balance sheet as well? I'm just trying to make sense of it all. Any help would be appreciated.
GoodBuy must determine how many cell phones and recorders should be produced during December. Demand is large enough to ensure that all goods produced will be sold. All sales are on credit, however, and payment for goods produced in December will not be received until February 1, 2009. During December, GoodBuy will collect $2000 in accounts receivable, and GoodBuy must pay off $1000 of the outstanding loan and a monthly rent of $1000. On January 1, 2009, GoodBuy will receive a shipment of raw material worth $2000, which will be paid for on February 1, 2009.
GoodBuy’s management has decided that the cash balance on January 1, 2009 must be at least $4000. To maintain its current favorable credit status, GoodBuy’s bank requires that the current ratio at the beginning of January be at least 2. To maximize the contribution to profit from December production, (revenues to be received – variable production costs), what should GoodBuy produce during December?
Cost Information for GoodBuy
Cell Phones | Recorders | |
Selling Price | $100 | $90 |
Labor Cost | $50 | $35 |
Raw Material Cost | $30 | $40 |
Balance Sheet for GoodBuy
| Assets | Liabilities | |
| Cash | $10,000 | |
| Accounts Receivable1 | $3,000 | |
| Inventory Outstanding2 | $7,000 | |
| Bank Loan | $10,000 |
1 – Accounts receivable is money owed to GoodBuy by customers who have previously purchased GoodBuy products.
2 – Value of December 1, 2008 inventory = 30(100) + 40(100) = $7000.
Deliverables:
- A complete algebraic formulation of the linear programming model. This should include a description of the decision variables and an explanation of the objective function and constraints.
- Computer output of your solution and ranging from POM-QM. This must be printed from POM-QM.
- A report (MS-Word document) to management describing your objective and production plan. The report should be written clearly, concisely, and accurately. It should fit on a single page. Many young professionals believe that they will be evaluated entirely on whether the numbers are right and this is simply not true. Managers are busy people who have little time or patience to wade through poorly written reports. You will be graded on both grammatical and technical accuracy.
Hints and Suggestions
- You must determine how many cell phones and digital recorders to produce during December. Thus, you should define:
X1 = number of cell phones produced during December
X2 = number of digital recorders produced during December
- There are two constraints based on the availability of raw materials. In addition, GoodBuy faces the following two constraints:
- Cash on hand on January 1, 2009 must be at least $4000.
January 1 cash on hand = December 1 cash on hand
+ accounts receivable collected during December
- portion of loan repaid during December – December rent
- (January 1 assets)/(January 1 liabilities) ≥ 2 must hold.
Important Relationships
January 1 asset position = January cash position
+ January 1 accounts receivable + January 1 inventory position.
January 1 cash position = 10,000 – 50x1 – 35x2
January 1 accounts receivable = December 1 accounts receivable
+ accounts receivable from December sales
- accounts receivable collected during December.
Value of January 1 inventory = value of December 1 inventory
- value of inventory used in December
+ value of inventory received on January 1.
January 1 liabilities = December 1 liabilities – December loan payment
+ amount due on January 1 inventory shipment.
Your mathematical result should be:
X1 = 50 cell phones
X2 = 100 digital recorders
Maximum profit = $2500.
Here's all the infromation associated with the problem. Here's what I have so far:
objective: max
let x1= #of cell phones produced during december
x2= #of digital recorders produced during decmeber
x3= labor costs
x4= raw material cost
x5= cash on hand
x6= A/R
x7= inventory on hand
x8- loan
x9= rent
Subject to:
50x3+30x4 <100 (cell phones)
35x3 + 40x4 < 100 (recorders)
10,000x5 + 2000x6 - 1000x8 - 1000x9 - x3 > 4,000 (cash in hand)
Should l I have that many variables (x1, x2, x3, x4) ? And as far as my objective goes should it include what's in the balance sheet as well? I'm just trying to make sense of it all. Any help would be appreciated.